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Prove by mathematical induction that 1+3...

Prove by mathematical induction that
`1+3+3^2+…………+3^(n-1)=(3^n -1)/2`

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JBD PUBLICATION-MODEL PAPER (8)-EXERICSE
  1. If y=f(x)=(2x+3)/(5x-2), prove that f(y)=x.

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  2. If sin theta= n sin(theta+2 alpha), show that : tan(theta+ alpha)=(1+n...

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  3. Prove by mathematical induction that 1+3+3^2+…………+3^(n-1)=(3^n -1)/2

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  4. Find the number of words which can be made by using all the letters of...

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  5. If C(n,10)=C(n,12), determine n and hence C(n,5).

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  6. The A.M. between two positive numbers is 34 and their G.M. is 16. find...

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  7. If (a^n+b^n)/(a^(n-1)+b^(n-1)) is the A.M. between a and b, then find ...

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  8. Find the equations of the lines, which pass through the point (4, 5) a...

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  9. Find the area of the triangle formed by the lines joining the vertex o...

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  10. Evaluate: underset(xrarr1)lim (3x^2-2x-10)/(x^2-4).

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  11. Find the derivative of (x^(n)-a^(n))/(x-a) for some constant a, x ne...

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  12. A card is drawn from a well shuffled pack of 52 cards. Find the probab...

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  13. A card is drawn from a well shuffled pack of 52 cards. Find the probab...

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  14. If z=x+iy and |(z-3)/(z+3)| = 2, show that x^2+y^2+10x+9=0.

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  15. If (1-7i)/(2i)^2= a+ib, then find the value of a and b.

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  16. Give the graphical solution of the following system of inequalities: 2...

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  17. Find all pairs of positive integers such that their sum is less than 8...

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  18. Evaluate underset(x rarr 0)lim(sin ax+bx)/(ax+sin bx)

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  19. Find the derivative secx w.r.t x

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  20. The mean and standard deviation of 20 observations are found to be 10 ...

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